Spinning particles on 2-sphere in accord with the Bianchi classification

Abstract

Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of spinning particles on 2-sphere, the spin degrees of freedom of which are represented by a 3-vector obeying the structure relations of a 3d real Lie algebra. Generalisations involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar extensions, which rely upon d=4,5,6 real Lie algebras, is elucidated.

13 pages

References in corpus (6)

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• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Supersymmetric many-body Euler-Calogero-Moser model
• N=4 superconformal mechanics from the su(2) perspective
• Spinning extensions of $D(2,1;\alpha )$ superconformal mechanics
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